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Number of solutions of a trig-root equation

High school · ●●○○○ 20 pts

Find the number of real solutions xx of the equation sin⁡(πx4)+cos⁡(π2−x4)=2\sin\left(\frac{\pi\sqrt x}{4}\right)+\cos\left(\frac{\pi\sqrt{2-x}}{4}\right)=\sqrt 2.

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monotonicityintermediate value theoremderivativesdomain of square roots